Energy and area minimizers in metric spaces
Published in:
- Advances in Calculus of Variations. - 2016, vol. 10, no. 4, p. 407–421
English
We show that in the setting of proper metric spaces one obtains a solution of the classical 2-dimensional Plateau problem by minimizing the energy, as in the classical case, once a definition of area has been chosen appropriately. We prove the quasi- convexity of this new definition of area. Under the assumption of a quadratic isoperimetric inequality we establish regularity results for energy minimizers and improve Hölder exponents of some area-minimizing discs.
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Faculty
- Faculté des sciences et de médecine
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Department
- Département de Mathématiques
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Language
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Classification
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Mathematics
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License
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License undefined
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Identifiers
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Persistent URL
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https://folia.unifr.ch/unifr/documents/306168
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